Financial Management



Corporate Finance

MBAC 6060

Jaime Zender

Problem Set #6

(1) Suppose there are two stocks you are considering investing in, Stock A and Stock B. The relevant information on these assets is given below:

|State of the |Probability of |Return on security |Return on security |

|Economy |the state |A |B |

|Bear |0.4 |3% |6.5% |

|Bull |0.6 |15% |6.5% |

(A) Calculate the expected returns and the standard deviations of the two securities.

(B) If you invest $2,500 in security A and $3,500 in security B what will be the expected return and standard deviation of you portfolio.

(C) You borrow 40 shares of stock B from someone and sell these shares at the current market price of $50 per share, promising to return 40 shares in a year (this is a short sale). Then you used all the proceeds of this short sale plus your own $6,000 and bought security A. What is the expected return and standard deviation of this position?

(2) Consider the three assets, A, B, and C. They have expected returns given as E(RA) = 10%, E(RB) = 5%, and E(RC) = 15%. Their variances and covariances are given in the following matrix:

|Assets |A |B |C |

|A | .05 |------- |------- |

|B |-.009 |.04 |------- |

|C |+.006 |-.010 |.06 |

A) Calculate the expected return and the variance for a portfolio of these three assets that is worth a total of $200,000 with investments of $100,000 in asset A and $50,000 in assets B and C. Compare this portfolio to owning asset A alone. What is responsible for the difference?

B) Suppose we have an equally weighted portfolio instead, what is this portfolio’s expected return and variance? Explain the difference from the portfolio in part (A).

(3) You are a very conservative investor. You hold only a total market index mutual fund and T-bills. Currently the market index has an expected return of 12% and a standard deviation of 20% and the T-bills promise a 4% return. You are evaluating the desirability of three different portfolios, 100% in the market index, 75% in the index and 25% in T-bills, and 50% in each.

A) What is the expected return and standard deviation of each of the three candidate portfolios?

B) What is the beta of each of the three portfolios?

C) What is the risk premium on the index portfolio?

D) What criterion would you use to choose between the three candidates?

E) What are the expected return, standard deviation, and beta of your portfolio if you have $100,000 of your own to invest and you borrow another $100,000 at the risk free rate so you can buy $200,000 of the market index?

(4) You form a portfolio of six individual stocks, numbered 1 – 6. These stocks have betas given as: (1 = .6, (2 = .9, (3 = 1.0, (4 = 1.1, (5 = 1.2, (6 = 1.4. You choose portfolio weights given as: w1 = .2, w2 = .1, w3 = .3, w4 = .1, w5 = .2, and w6 = .1.

A) What is the beta of your portfolio?

B) Computing the beta of the portfolio as in (A) tells us what about the way an individual asset contributes to the risk of a portfolio?

C) If the risk free rate is 5% and the expected return on the market portfolio is 13% what is the expected return on your portfolio?

D) If the market portfolio has a variance of 0.0441 can you determine what the total risk of your portfolio will be? What can you tell about your portfolio’s risk characteristics?

E) If you change to an equally weighted portfolio of these six stocks what will be the expected return on your new portfolio? Why the change?

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